Intersphinx for cvxopt, cvxpy, cypari2, cysignals, flint, fpylll, gmpy2, ipywidgets, matplotlib, mpmath, networkx, numpy, rpy2, scipy, sympy

src/doc/en/developer/sage_manuals.rst

@@ -38,7 +38,7 @@ Sage's manuals are written in `ReST <http://docutils.sourceforge.net/rst.html>`_
   ``SAGE_ROOT/src/doc/en``.
 
 - Some documents have been **translated** into other languages. In order to
-  access them, change en/ into fr/,es/, de/... See :ref:`section-manuals-names`.
+  access them, change ``en/`` into ``fr/``, ``es/``, ``de/``... See :ref:`section-manuals-names`.
 
 .. _section-manuals-edit:
 
@@ -82,9 +82,12 @@ The documentation can contain links toward modules, classes, or methods, e.g.::
     :mod:`link to a module <sage.module_name>`
     :mod:`sage.module_name` (here the link's text is the module's name)
 
-For links toward classes, methods, or function, replace **:mod:** by
-**:class:**, **:meth:** or **:func:** respectively.  See `Sphinx' documentation
-<https://www.sphinx-doc.org/en/master/usage/restructuredtext/roles.html>`_.
+For links toward classes, methods, or functions, replace ``:mod:`` by
+``:class:``, ``:meth:``, or ``:func:``, respectively.  See Sphinx' documentation
+on `cross-referencing Python objects
+<https://www.sphinx-doc.org/en/master/usage/domains/python.html#cross-referencing-python-objects>`_
+and for the general syntax of
+`roles <https://www.sphinx-doc.org/en/master/usage/restructuredtext/roles.html>`_.
 
 **Short links:** the link ``:func:`~sage.mod1.mod2.mod3.func1``` is equivalent
 to ``:func:`func1 <sage.mod1.mod2.mod3.func1>```: the function's name will be
@@ -94,6 +97,72 @@ used as the link name, instead of its full path.
 absolute. If you are documenting ``method_one``, you can write
 ``:meth:`method_two```.
 
+**Intersphinx references:** in the same way, you can refer to the modules, classes,
+methods, functions of the Python standard library and of several Python packages
+used by SageMath; see the `Intersphinx documentation
+<https://www.sphinx-doc.org/en/master/usage/extensions/intersphinx.html>`_
+for details. Likewise, you can refer to the C functions of the
+:ref:`FLINT <spkg_flint>` library; see `Sphinx' documentation on
+cross-referencing C constructs
+<https://www.sphinx-doc.org/en/master/usage/domains/c.html#cross-referencing-c-constructs>`_
+for more information.
+
+.. LIST-TABLE::
+   :widths: 4 7 5
+   :header-rows: 0
+
+   * - Python
+     - ``:exc:`ValueError```
+     - :exc:`ValueError`
+   * - :ref:`CVXOPT <spkg_cvxopt>`
+     - ``:func:`cvxopt.solvers.socp```
+     - :func:`cvxopt.solvers.socp`
+   * - :ref:`CVXpy <spkg_cvxpy>`
+     - ``:class:`~cvxpy.atoms.log_det.log_det```
+     - :class:`~cvxpy.atoms.log_det.log_det`
+   * - :ref:`cypari2 <spkg_cypari>`
+     - ``:class:`cypari2.gen.Gen```
+     - :class:`cypari2.gen.Gen`
+   * - :ref:`cysignals <spkg_cysignals>`
+     - ``:envvar:`CYSIGNALS_CRASH_DAYS```
+     - :envvar:`CYSIGNALS_CRASH_DAYS`
+   * - :ref:`FLINT <spkg_flint>`
+     - ``:c:func:`arith_bell_number```
+     - :c:func:`arith_bell_number`
+   * - :ref:`gmpy2 <spkg_gmpy2>`
+     - ``:func:`gmpy2.gamma_inc```
+     - :func:`gmpy2.gamma_inc`
+   * - :ref:`ipywidgets <spkg_ipywidgets>`
+     - ``:mod:`~ipywidgets.widgets.widget_date```
+     - :mod:`~ipywidgets.widgets.widget_date`
+   * - :ref:`Matplotlib <spkg_matplotlib>`
+     - ``:mod:`matplotlib.bezier```
+     - :mod:`matplotlib.bezier`
+   * - :ref:`mpmath <spkg_mpmath>`
+     - ``:attr:`mpmath.mp.khinchin```
+     - :attr:`mpmath.mp.khinchin`
+   * - :ref:`NetworkX <spkg_networkx>`
+     - ``:attr:`~networkx.DiGraph.out_degree```
+     - :attr:`~networkx.DiGraph.out_degree`
+   * - :ref:`NumPy <spkg_numpy>`
+     - ``:data:`numpy.NAN```
+     - :data:`numpy.NAN`
+   * - :ref:`pplpy <spkg_pplpy>`
+     - ``:mod:`ppl.polyhedron```
+     - :mod:`ppl.polyhedron`
+   * - :ref:`rpy2 <spkg_rpy2>`
+     - ``:class:`~rpy2.robjects.vectors.DataFrame```
+     - :class:`~rpy2.robjects.vectors.DataFrame`
+   * - :ref:`SciPy <spkg_scipy>`
+     - ``:data:`scipy.special.huber```
+     - :data:`scipy.special.huber`
+   * - :ref:`SymPy <spkg_sympy>`
+     - ``:class:`~sympy.diffgeom.WedgeProduct```
+     - :class:`~sympy.diffgeom.WedgeProduct`
+
+To see the available cross references in any of these libraries, you can use the command
+``./sage -python -m sphinx.ext.intersphinx src/doc/common/_vendor/numpy.inv``.
+
 **Global namespace:** if an object (e.g. ``integral``) is automatically imported
 by Sage, you can link toward it without specifying its full path:
 

src/doc/en/reference/matrices/index.rst

@@ -29,7 +29,7 @@ following additional ways to compute with matrices:
 -  The GSL C-library is included with Sage, and can be used via
    Cython.
 
--  The ``scipy`` module provides support for
+-  The :mod:`scipy:scipy` module provides support for
    *sparse* numerical linear algebra, among many other things.
 
 -  The ``numpy`` module, which you load by typing

src/sage/calculus/desolvers.py

@@ -27,8 +27,8 @@
   order equations, return list of points.
 
 - :func:`desolve_odeint` - Solve numerically a system of first-order ordinary
-  differential equations using ``odeint`` from `scipy.integrate module.
-  <https://docs.scipy.org/doc/scipy/reference/integrate.html#module-scipy.integrate>`_
+  differential equations using :func:`~scipy:scipy.integrate.odeint` from
+  the module :mod:`scipy:scipy.integrate`.
 
 - :func:`desolve_system` - Solve a system of 1st order ODEs of any size using
   Maxima. Initial conditions are optional.
@@ -1499,7 +1499,7 @@ def desolve_odeint(des, ics, times, dvars, ivar=None, compute_jac=False, args=()
                    mxstep=0, mxhnil=0, mxordn=12, mxords=5, printmessg=0):
     r"""
     Solve numerically a system of first-order ordinary differential equations
-    using ``odeint`` from scipy.integrate module.
+    using :func:`scipy:scipy.integrate.odeint`.
 
     INPUT:
 
@@ -1517,8 +1517,9 @@ def desolve_odeint(des, ics, times, dvars, ivar=None, compute_jac=False, args=()
     - ``compute_jac`` -- boolean. If True, the Jacobian of ``des`` is computed and
       used during the integration of stiff systems. Default value is False.
 
-    Other Parameters (taken from the documentation of odeint function from `scipy.integrate module.
-    <https://docs.scipy.org/doc/scipy/reference/integrate.html#module-scipy.integrate>`_)
+    Other Parameters (taken from the documentation of the
+    :func:`~scipy:scipy.integrate.odeint` function from
+    :mod:`scipy:scipy.integrate`):
 
     - ``rtol``, ``atol`` : float
       The input parameters ``rtol`` and ``atol`` determine the error

src/sage/graphs/generators/families.py

@@ -513,12 +513,13 @@ def BalancedTree(r, h):
     OUTPUT:
 
     The perfectly balanced tree of height `h \geq 1` and whose root has
-    degree `r \geq 2`. A ``NetworkXError`` is returned if `r < 2` or
-    `h < 1`.
+    degree `r \geq 2`. A :exc:`~networkx.exception.NetworkXError` is raised
+    if `r < 2` or `h < 1`.
 
     ALGORITHM:
 
-    Uses `NetworkX <http://networkx.lanl.gov>`_.
+    Uses the :ref:`NetworkX <spkg_networkx>` function
+    :func:`~networkx.generators.classic.balanced_tree`.
 
     EXAMPLES:
 

src/sage/graphs/generic_graph.py

@@ -1336,9 +1336,9 @@ def export_to_file(self, filename, format=None, **kwds):
 
         - ``format`` -- string (default: ``None``); select the output format
           explicitly. If set to ``None`` (default), the format is set to be the
-          file extension of ``filename``. Admissible formats are: ``adjlist``,
-          ``dot``, ``edgelist``, ``gexf``, ``gml``, ``graphml``,
-          ``multiline_adjlist``, ``pajek``, ``yaml``.
+          file extension of ``filename``. Admissible formats are: ``'adjlist'``,
+          ``'dot'``, ``'edgelist'``, ``'gexf'``, ``'gml'``, ``'graphml'``,
+          ``'multiline_adjlist'``, ``'pajek'``.
 
         - All other arguments are forwarded to the subfunction. For more
           information, see their respective documentation:
@@ -1348,15 +1348,14 @@ def export_to_file(self, filename, format=None, **kwds):
               :widths: 30, 70
               :delim: |
 
-              ``adjlist`` | http://networkx.lanl.gov/reference/generated/networkx.readwrite.adjlist.write_adjlist.html
-              ``dot`` | https://networkx.github.io/documentation/latest/reference/generated/networkx.drawing.nx_pydot.write_dot.html
-              ``edgelist`` | http://networkx.lanl.gov/reference/generated/networkx.readwrite.edgelist.write_edgelist.html
-              ``gexf`` | http://networkx.lanl.gov/reference/generated/networkx.readwrite.gexf.write_gexf.html
-              ``gml`` | http://networkx.lanl.gov/reference/generated/networkx.readwrite.gml.write_gml.html
-              ``graphml`` | http://networkx.lanl.gov/reference/generated/networkx.readwrite.graphml.write_graphml.html
-              ``multiline_adjlist`` | http://networkx.lanl.gov/reference/generated/networkx.readwrite.multiline_adjlist.write_multiline_adjlist.html
-              ``pajek`` | http://networkx.lanl.gov/reference/generated/networkx.readwrite.pajek.write_pajek.html
-              ``yaml`` | http://networkx.lanl.gov/reference/generated/networkx.readwrite.nx_yaml.write_yaml.html
+              ``'adjlist'``           | :func:`networkx.readwrite.adjlist.write_adjlist`
+              ``'dot'``               | :func:`networkx.drawing.nx_pydot.write_dot`
+              ``'edgelist'``          | :func:`networkx.readwrite.edgelist.write_edgelist`
+              ``'gexf'``              | :func:`networkx.readwrite.gexf.write_gexf`
+              ``'gml'``               | :func:`networkx.readwrite.gml.write_gml`
+              ``'graphml'``           | :func:`networkx.readwrite.graphml.write_graphml`
+              ``'multiline_adjlist'`` | :func:`networkx.readwrite.multiline_adjlist.write_multiline_adjlist`
+              ``'pajek'``             | :func:`networkx.readwrite.pajek.write_pajek`
 
         .. SEEALSO::
 
@@ -1366,7 +1365,7 @@ def export_to_file(self, filename, format=None, **kwds):
         .. NOTE::
 
             This functions uses the ``write_*`` functions defined in NetworkX
-            (see http://networkx.lanl.gov/reference/readwrite.html).
+            (see :mod:`networkx.readwrite`).
 
         EXAMPLES::
 

src/sage/libs/flint/arith_sage.pyx

@@ -31,6 +31,10 @@ def bell_number(unsigned long n):
 
     See :wikipedia:`Bell_number`.
 
+    ALGORITHM:
+
+    Uses :c:func:`arith_bell_number`.
+
     EXAMPLES::
 
         sage: from sage.libs.flint.arith_sage import bell_number

src/sage/manifolds/differentiable/integrated_curve.py

@@ -949,7 +949,7 @@ def solve(self, step=None, method='odeint', solution_key=None,
           use for the integration of the curve; available algorithms are:
 
           * ``'odeint'`` - makes use of
-            `scipy.integrate.odeint <https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.odeint.html>`_
+            :func:`scipy:scipy.integrate.odeint`
             via Sage solver
             :func:`~sage.calculus.desolvers.desolve_odeint`; ``odeint`` invokes
             the LSODA algorithm of the
@@ -961,9 +961,9 @@ def solve(self, step=None, method='odeint', solution_key=None,
             makes use of Maxima's dynamics package via Sage solver
             :func:`~sage.calculus.desolvers.desolve_system_rk4` (quite slow)
           * ``'dopri5'`` - Dormand-Prince Runge-Kutta of order (4)5 provided by
-            `scipy.integrate.ode <https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.ode.html>`_
+            :obj:`scipy:scipy.integrate.ode`
           * ``'dop853'`` - Dormand-Prince Runge-Kutta of order 8(5,3) provided by
-            `scipy.integrate.ode <https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.ode.html>`_
+            :obj:`scipy:scipy.integrate.ode`
 
           and those provided by ``GSL`` via Sage class
           :class:`~sage.calculus.ode.ode_solver`:
@@ -1425,8 +1425,8 @@ def solve_across_charts(self, charts=None, step=None, solution_key=None,
         Integrate the curve numerically over the domain of integration, with
         the ability to switch chart mid-integration.
 
-        The only supported solver is
-        `scipy.integrate.ode <https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.ode.html>`_, because it supports basic event handling, needed to detect when the
+        The only supported solver is :obj:`scipy:scipy.integrate.ode`,
+        because it supports basic event handling, needed to detect when the
         curve is reaching the frontier of the chart. This is an adaptive step
         solver. So the ``step`` is not the step of integration but instead the
         step used to peak at the current chart, and switch if needed.
@@ -1525,8 +1525,8 @@ def solve_across_charts(self, charts=None, step=None, solution_key=None,
 
         The integration is done as usual, but using the method
         :meth:`solve_across_charts` instead of :meth:`solve`. This forces the
-        use of ``scipy.integrate.ode`` as the solver, because of event handling
-        support.
+        use of :obj:`scipy:scipy.integrate.ode` as the solver, because of event
+        handling support.
 
         The argument ``verbose=True`` will cause the solver to write a small
         message each time it is switching chart::

src/sage/matrix/matrix_double_dense.pyx

@@ -594,8 +594,8 @@ cdef class Matrix_double_dense(Matrix_numpy_dense):
 
         ALGORITHM:
 
-        Computation is performed by the ``norm()`` function of
-        the SciPy/NumPy library.
+        Computation is performed by the :func:`~scipy:scipy.linalg.norm`
+        function of the SciPy/NumPy library.
 
         EXAMPLES:
 
@@ -739,7 +739,7 @@ cdef class Matrix_double_dense(Matrix_numpy_dense):
         ALGORITHM:
 
         The singular values come from the SVD decomposition
-        computed by SciPy/NumPy.
+        computed by SciPy/NumPy using :func:`scipy:scipy.linalg.svd`.
 
         EXAMPLES:
 
@@ -1073,17 +1073,17 @@ cdef class Matrix_double_dense(Matrix_numpy_dense):
 
           - ``'default'`` - applicable to any matrix
             with double-precision floating point entries.
-            Uses the :meth:`~scipy.linalg.eigvals` method from SciPy.
+            Uses the :func:`~scipy:scipy.linalg.eigvals` function from SciPy.
 
           - ``'symmetric'`` - converts the matrix into a real matrix
             (i.e. with entries from :class:`~sage.rings.real_double.RDF`),
             then applies the algorithm for Hermitian matrices.  This
             algorithm can be significantly faster than the
             ``'default'`` algorithm.
 
-          - ``'hermitian'`` - uses the :meth:`~scipy.linalg.eigh` method
-            from SciPy, which applies only to real symmetric or complex
-            Hermitian matrices.  Since Hermitian is defined as a matrix
+          - ``'hermitian'`` - uses the :func:`~scipy:scipy.linalg.eigh`
+            function from SciPy, which applies only to real symmetric or
+            complex Hermitian matrices.  Since Hermitian is defined as a matrix
             equaling its conjugate-transpose, for a matrix with real
             entries this property is equivalent to being symmetric.
             This algorithm can be significantly faster than the
@@ -1707,6 +1707,10 @@ cdef class Matrix_double_dense(Matrix_numpy_dense):
         Find a solution `X` to the equation `A X = B` if ``self`` is a square
         matrix `A`.
 
+        ALGORITHM:
+
+        Uses the function :func:`scipy:scipy.linalg.solve` from SciPy.
+
         TESTS::
 
             sage: # needs sage.symbolic
@@ -1730,6 +1734,10 @@ cdef class Matrix_double_dense(Matrix_numpy_dense):
         Compute a least-squares solution `X` to the equation `A X = B` where
         ``self`` is the matrix `A`.
 
+        ALGORITHM:
+
+        Uses the function :func:`scipy:scipy.linalg.lstsq` from SciPy.
+
         TESTS::
 
             sage: A = matrix(RDF, 3, 2, [1, 3, 4, 2, 0, -3])
@@ -1754,7 +1762,7 @@ cdef class Matrix_double_dense(Matrix_numpy_dense):
 
         ALGORITHM:
 
-        Use numpy
+        Uses :func:`scipy:scipy.linalg.det`.
 
         EXAMPLES::
 
@@ -2037,7 +2045,7 @@ cdef class Matrix_double_dense(Matrix_numpy_dense):
 
         ALGORITHM:
 
-        Calls "linalg.qr" from SciPy, which is in turn an
+        Calls :func:`scipy:scipy.linalg.qr` from SciPy, which is in turn an
         interface to LAPACK routines.
 
         EXAMPLES:

src/sage/matroids/matroids_plot_helpers.py

@@ -20,8 +20,9 @@
     via an optimization that gives aesthetically pleasing point placement (in
     some sense. This is not yet implemented).    One can then use
     ``createline`` function to produce sequence of ``100`` points on a smooth
-    curve containing the points in the specified line which inturn uses
-    ``scipy.interpolate.splprep`` and ``scipy.interpolate.splev``.  Then one
+    curve containing the points in the specified line which in turn uses
+    :func:`scipy:scipy.interpolate.splprep` and
+    :func:`scipy:scipy.interpolate.splev`.  Then one
     can use sage's graphics primitives ``line``, ``point``, ``text`` and
     ``points`` to produce graphics object containing points (ground set
     elements) and lines (for a rank 3 matroid, these are flats of rank 2 of

src/sage/modules/vector_double_dense.pyx

@@ -395,8 +395,8 @@ cdef class Vector_double_dense(Vector_numpy_dense):
 
         ALGORITHM:
 
-        Computation is performed by the ``norm()`` function of
-        the SciPy/NumPy library.
+        Computation is performed by the :func:`~scipy:scipy.linalg.norm`
+        function of the SciPy/NumPy library.
 
         EXAMPLES: